Nonextensive thermodynamics of the two-site Hubbard model

Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature T to the Lagrange multiplier β, two methods have been adopted: T=1/kBβ in method A [Tsallis et al., Physica A 261 (1998) 534], and T=cq/kBβ in method B [Abe et al., Phys. Lett. A 281 (2001) 126], where kB denotes the Boltzman constant, cq=∑ipiq,pi the probability distribution of the ith state, and q the entropic index. Temperature dependences of specific heat and magnetic susceptibility have been calculated for 1⩽q⩽2, the conventional Boltzman-Gibbs statistics being recovered in the limit of q=1. The Curie constant Γq of the susceptibility in the atomic and low-temperature limits (t/U→0,T/U→0) is shown to be given by Γq=2q22(q-1) in method A, and Γq=2q in method B, where t stands for electron hoppings and U intra-atomic interaction in the Hubbard model. These expressions for Γq are shown to agree with the results of a free spin model which have been studied also by the NES with methods A and B. A comparison has been made between the results for canonical and grand-canonical ensembles of the model.